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环拓扑（影印版）

样章
作者：
Victor M. Buchstaber, Taras E. Panov
定价：
199.00 元
版面字数：
860千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2023年
ISBN：
978-7-04-059299-3
物料号：
59299-00
出版时间：
2023-03-08
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
拓扑学
暂无
  • 目录
    • 前辅文
      • Chapter 1. Geometry and Combinatorics of Polytopes
        • 1.1. Convex polytopes
          • 1.2. Gale duality and Gale diagrams
            • 1.3. Face vectors and Dehn–Sommerville relations
              • 1.4. Characterising the face vectors of polytopes
                • Polytopes: Additional Topics
                  • 1.5. Nestohedra and graph-associahedra
                    • 1.6. Flagtopes and truncated cubes
                      • 1.7. Differential algebra of combinatorial polytopes
                        • 1.8. Families of polytopes and differential equations
                        • Chapter 2. Combinatorial Structures
                          • 2.1. Polyhedral fans
                            • 2.2. Simplicial complexes
                              • 2.3. Barycentric subdivision and flag complexes
                                • 2.4. Alexander duality
                                  • 2.5. Classes of triangulated spheres
                                    • 2.6. Triangulated manifolds
                                      • 2.7. Stellar subdivisions and bistellar moves
                                        • 2.8. Simplicial posets and simplicial cell complexes
                                          • 2.9. Cubical complexes
                                          • Chapter 3. Combinatorial Algebra of Face Rings
                                            • 3.1. Face rings of simplicial complexes
                                              • 3.2. Tor-algebras and Betti numbers
                                                • 3.3. Cohen–Macaulay complexes
                                                  • 3.4. Gorenstein complexes and Dehn–Sommerville relations
                                                    • 3.5. Face rings of simplicial posets
                                                      • Face Rings: Additional Topics
                                                        • 3.6. Cohen–Macaulay simplicial posets
                                                          • 3.7. Gorenstein simplicial posets
                                                            • 3.8. Generalised Dehn–Sommerville relations
                                                            • Chapter 4. Moment-Angle Complexes
                                                              • 4.1. Basic definitions
                                                                • 4.2. Polyhedral products
                                                                  • 4.3. Homotopical properties
                                                                    • 4.4. Cell decomposition
                                                                      • 4.5. Cohomology ring
                                                                        • 4.6. Bigraded Betti numbers
                                                                          • 4.7. Coordinate subspace arrangements
                                                                            • Moment-Angle Complexes: Additional Topics
                                                                              • 4.8. Free and almost free torus actions on moment-angle complexes
                                                                                • 4.9. Massey products in the cohomology of moment-angle complexes
                                                                                  • 4.10. Moment-angle complexes from simplicial posets
                                                                                  • Chapter 5. Toric Varieties and Manifolds
                                                                                    • 5.1. Classical construction from rational fans
                                                                                      • 5.2. Projective toric varieties and polytopes
                                                                                        • 5.3. Cohomology of toric manifolds
                                                                                          • 5.4. Algebraic quotient construction
                                                                                            • 5.5. Hamiltonian actions and symplectic reduction
                                                                                            • Chapter 6. Geometric Structures on Moment-Angle Manifolds
                                                                                              • 6.1. Intersections of quadrics
                                                                                                • 6.2. Moment-angle manifolds from polytopes
                                                                                                  • 6.3. Symplectic reduction and moment maps revisited
                                                                                                    • 6.4. Complex structures on intersections of quadrics
                                                                                                      • 6.5. Moment-angle manifolds from simplicial fans
                                                                                                        • 6.6. Complex structures on moment-angle manifolds
                                                                                                          • 6.7. Holomorphic principal bundles and Dolbeault cohomology
                                                                                                            • 6.8. Hamiltonian-minimal Lagrangian submanifolds
                                                                                                            • Chapter 7. Half-Dimensional Torus Actions
                                                                                                              • 7.1. Locally standard actions and manifolds with corners
                                                                                                                • 7.2. Toric manifolds and their quotients
                                                                                                                  • 7.3. Quasitoric manifolds
                                                                                                                    • 7.4. Locally standard T-manifolds and torus manifolds
                                                                                                                      • 7.5. Topological toric manifolds
                                                                                                                        • 7.6. Relationship between different classes of T-manifolds
                                                                                                                          • 7.7. Bounded flag manifolds
                                                                                                                            • 7.8. Bott towers
                                                                                                                              • 7.9. Weight graphs
                                                                                                                              • Chapter 8. Homotopy Theory of Polyhedral Products
                                                                                                                                • 8.1. Rational homotopy theory of polyhedral products
                                                                                                                                  • 8.2. Wedges of spheres and connected sums of sphere products
                                                                                                                                    • 8.3. Stable decompositions of polyhedral products
                                                                                                                                      • 8.4. Loop spaces, Whitehead and Samelson products
                                                                                                                                        • 8.5. The case of flag complexes
                                                                                                                                        • Chapter 9. Torus Actions and Complex Cobordism
                                                                                                                                          • 9.1. Toric and quasitoric representatives in complex bordism classes
                                                                                                                                            • 9.2. The universal toric genus
                                                                                                                                              • 9.3. Equivariant genera, rigidity and fibre multiplicativity
                                                                                                                                                • 9.4. Isolated fixed points: localisation formulae
                                                                                                                                                  • 9.5. Quasitoric manifolds and genera
                                                                                                                                                    • 9.6. Genera for homogeneous spaces of compact Lie groups
                                                                                                                                                      • 9.7. Rigid genera and functional equations
                                                                                                                                                      • Appendix A. Commutative and Homological Algebra
                                                                                                                                                        • A.1. Algebras and modules
                                                                                                                                                          • A.2. Homological theory of graded rings and modules
                                                                                                                                                            • A.3. Regular sequences and Cohen–Macaulay algebras
                                                                                                                                                              • A.4. Formality and Massey products
                                                                                                                                                              • Appendix B. Algebraic Topology
                                                                                                                                                                • B.1. Homotopy and homology
                                                                                                                                                                  • B.2. Elements of rational homotopy theory
                                                                                                                                                                    • B.3. Eilenberg–Moore spectral sequences
                                                                                                                                                                      • B.4. Group actions and equivariant topology
                                                                                                                                                                        • B.5. Stably complex structures
                                                                                                                                                                          • B.6. Weights and signs of torus actions
                                                                                                                                                                          • Appendix C. Categorical Constructions
                                                                                                                                                                            • C.1. Diagrams and model categories
                                                                                                                                                                              • C.2. Algebraic model categories
                                                                                                                                                                                • C.3. Homotopy limits and colimits
                                                                                                                                                                                • Appendix D. Bordism and Cobordism
                                                                                                                                                                                  • D.1. Bordism of manifolds
                                                                                                                                                                                    • D.2. Thom spaces and cobordism functors
                                                                                                                                                                                      • D.3. Oriented and complex bordism
                                                                                                                                                                                        • D.4. Characteristic classes and numbers
                                                                                                                                                                                          • D.5. Structure results
                                                                                                                                                                                            • D.6. Ring generators
                                                                                                                                                                                            • Appendix E. Formal Group Laws and Hirzebruch Genera
                                                                                                                                                                                              • E.1. Elements of the theory of formal group laws
                                                                                                                                                                                                • E.2. Formal group law of geometric cobordisms
                                                                                                                                                                                                  • E.3. Hirzebruch genera (complex case)
                                                                                                                                                                                                    • E.4. Hirzebruch genera (oriented case)
                                                                                                                                                                                                      • E.5. Krichever genus
                                                                                                                                                                                                      • Bibliography
                                                                                                                                                                                                        • Index

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